Lecture: From Algebra to Geometry

Caucher Birkar


Since the ancient times people have tried to understand systems of polynomial equations for practical and/or abstract reasons. It was slowly understood that geometry can be used to understand such equations by "graphing" their solutions in some appropriate space. The geometric picture provides a window for our intuition to guide us in how to investigate the qualitative nature of the solutions while algebra provides the machinery for rigorous proofs. In this talk I will try to explain some aspects of this story in simple terms.